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| MECA0489-1 | Analytical mechanics II
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| Duration : | 12h Th, 15h Pr |
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| Number of credits : |
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| Lecturer : | Jean Surdej |
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Language(s) of instruction :
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| French language |
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Organisation and examination :
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| Teaching in the first semester, examination in June with partial in January |
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Course contents :
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| The Lagrangian formulation of mechanics is intimately connected to the introduction of generalized coordinates which are used to describe the motion of a system of particles (including the solids) by elimination of possible constraints restricting their motions.
We first introduce the Lagrange's equations and apply this formalism to several different problems (cf. study of the symmetric top known as the Lagrange-Poisson problem, etc.). Then, we consider the symmetries of a problem and determine which are the associated quantities that are being preserved, via the application of Noether's theorem. The Hamilton variational problem is also discussed.
The chapter covering special relativity starts with a brief description of the difficulties encountered while attempting to interpret various physical experiments at the end of the XIXth century. We then introduce the Lorentz transformations. |
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Learning outcomes of the course :
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| At the end of this course, the students will be able to solve all kinds of problems in analytical mechanics, with and without holonomic constraints, using the Lagrange equations. Finally, the introduction to the Lorentz transformations in special relativity will help them to cast doubts on their classical notions of space and time, as well as on themselves. |
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Prerequisites and co-requisites/ Recommended optional programme components :
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| It is being assumed that the course of Analytical Mechanics I is familiar to the students. |
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Planned learning activities and teaching methods :
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| Practical exercices referring to the second part of the course of Analytical Mechanics will begin several weeks after the beginning of the theoretical course. They will take place during several after-noons according to a timetable that will be distributed in September. As far as possible, the physical principles presented during the theoretical courses will be illustrated by numerous examples selected for their importance in physics and in astronomy. |
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Mode of delivery (face-to-face ; distance-learning) :
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| In principle, the theoretical course begins with the start of the academic year. The lectures last 2h and take place once a week.The precise dates and location will become known to the students in early September. |
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Recommended or required readings :
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| Lecture notes as well as the "power-point" presentations projected during each lecture are accessible via the link http://www.aeos.ulg.ac.be/teaching.php
Reference books related to the course of Analytical Mechanics (2nd part) are (in French) :
- R. SIMON, Mécanique analytique, Volume 2 (1988), Editions Derouaux, Liège.
- J.W. Leech, Elements de Mécanique Analytique, 1961, Monographies Dunod, Paris.
- R. SIMON, Compléments de mécanique analytique, 1987, Editions Derouaux, Liège.
(in English) :
- J.W. Leech, Classical Mechanics, 1958, Butler and Tanner Ltd, Frome (printed in Great Britain)
- "Theory and Problems of Theoretical Mechanics" par Murray Spiegel (1967, Schaum Publishing Co.). |
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Assessment methods and criteria :
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| A written (2 exercises) and an oral exam (1 question, approximately 1h) will be proposed. Evaluation of the students will essentially be based upon his(her) understanding of the theory as opposed to his(her) memory skills. One test will be organized during the academic year. The results of this test will only be taken into account if it has a positive (no negative) impact on the final note (oral and practical exams) obtained by the student. |
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Work placement(s) :
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| None. |
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Organizational remarks :
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| None. |
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Contacts :
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| J. Surdej (Full Professor and F.R.S.-FNRS honorary research director).
Institute of Astrophysics and Geophysics, ULg, Allée du 6 Août 17, Bât. B5c, B-4000 Sart Tilman (Liège), Tel.: 04/366 97 83, Fax: 04-366 97 46, E-mail : surdej@astro.ulg.ac.be, WWW: http://www.aeos.ulg.ac.be/
Benoît Hubert, F.R.S.-FNRS Research Associate
Institut d'Astrophysique et de Géophysique
(local 2/18), Allée du 6 Août, 17
(Bât. B5c), B- 4000 Liège, Tél. :
04/3669727;
E-mail : B.Hubert@ulg.ac.be
Mme Sylvia Grandjean (Secretary): Sylvia.Grandjean@ulg.ac.be(Sylvia.Grandjean@astro.ulg.ac.be) |
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| Items online : |
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| Online notes (Meca II) |
| Videos of the lectures are accessible via Orbi. Lecture notes as well as the "power-point" presentations projected during each lecture are accessible in the form of PDF and/or PPS files via the link: |
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